Causality enforcing parametric heat transfer solvers for evolving geometries in advanced manufacturing

Abstract

We introduce a new method for solving parametric heat transfer partial differential equations on evolving geometries in advanced manufacturing applications. Physics-informed neural networks (PINNs) are a popular framework for integrating experimental data with known physical laws specified via partial differential equations (PDEs). Despite their increasing popularity, applying PINNs to manufacturing problems is limited compared to fluid and solid mechanics problems. The applications of PINNs acting as PDE solvers are absent where material is being added or removed. The objective of our work is to address this gap. By proposing a new loss function, we aim to expand the applications of PINNs for heat transfer to manufacturing problems with evolving geometries. Our method obviates the need for mesh-based discretization and time-marching schemes for evolving geometries. We consider predicting the transient temperature history in additive manufacturing as a single bead of material is deposited. We consider various evolving mixed Dirichlet and Neumann boundary condition cases to test our methodology. We verify our methodology by comparing our results with a validated finite element (FE) solver and observe that the results are in excellent agreement. Our method is naturally biased to respect causality, achieved by an automatic decrease in collocation point density as the geometry evolves. We extend our method to solve a parametric heat transfer equation for the single bead addition problem and outline the advantages in computational cost provided by our parametric solver compared to running multiple instances of an FE solver.